Good news : you are moving to London and you have just found your "Home Sweet Home". Bad news : you don't trust the estate agent and you are unsure how things will work from now on.
Don't panic! You will find below the main points to be aware of before signing your tenancy agreement.
First don't be surprised by the "referencing" process you will be going through, which is a mix of verifying your identity and your credit worthiness. This process is standard in the London rental market, and is valid for everyone, whether British or foreigners.
The referencing is usually conducted by an independent agency, in order to verify that you will have the financial means to afford your monthly rent. You will need to agree in writing for these checks to take place and you will also need to pay for it! The cost will depend on the agency, but generally it is not negotiable. In most cases, the referencing agency will check your annual salary with your UK employer, and ask your current landlord for a reference (positive, of course).
If the referencing comes back positive, then you will receive a draft rental contract from the estate agent, the Tenancy Agreement. This document regulates the obligations of the landlord and the tenant, and it must be checked before you sign it off, in order to avoid any problems in the future.
The Tenancy Agreement MUST contain the following elements, as a minimum:
The property address
The rental amount, and how to pay it
How and when the rent will be reviewed, when the time has come
Additional fees, if any
Start and end date of the tenancy
The holding deposit amount and with which scheme it will be deposited (this is very important)
The obligations of tenant and landlor (for example if you smoke or have a pet, check that it won't be an issue)
Don't hesitate to ask questions if something is not clear, or to negotiate any points which don't suit you (tenancy duration, break clause, pets, etc.). After signing it off, it will be too late!
Finally, check with the estate agent that the check-in inventory is planned, and you can move in with total peace of mind!